An Application of Chaos Theory to the High Frequency RCS Prediction of Engine Ducts

Conclusions

We establish a connection between the Lyapunov exponent and SB ray methods which places a limit on the ability to make numerically deterministic or convergent predictions. When this limit is reached the ray fields are essentially random. One method, valid for ergodic straight ducts, is to represent the random ray field component by a field composed of randomly directed plane waves. We demonstrate that predictions made under this assumption have very similar bistatic RCS characteristics to those of an accurate modal solution.

Estimates of the Lyapunov exponent are directly related to average ray divergence and hence average ray intensity. For ergodic ray tracing this can be determined by the tracing of a single ray in order to place limits on the ability to achieve convergence. The computational cost of estimating the Lyapunov exponent is usually negligible compared to the cost of a full RCS prediction where all the rays on the entry plane must be traced.